Find the potential function f for the field F. 2 +y F = -k 2 3 2.2 x +y +C O A. f(x.y.z) = 2 x+y O B. f(x.y.z) = +C 2 zx + OC. f(x.y.z) = Vx² +y? + In z+C 1 O D. f(x.y.z) = +C z?V +y?

Q: Find the gradient field F = Vo for the potential function o below. P(x,y,z) = In (x2 + 2y2 + z²)…

A: We have to find gradient of given function.

Q: gral of the field F(x,y,z) = 7xi + 7yj + 7zk across the portion of the sphere x2 +y² +z? = a? in the…

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Q: Q1(a) For which value of a the field v = (y-x)i +(2x- y)j+azk is solenoidal. (b) Find the gradient…

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Q: 10. Find a potential function for the vector field F(x, y, z) = 3x²i + j+ 2z In yk. A) 2³ + 2z In y…

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Q: (a) Show that the vector field F(x, y) = (x², y²) is conser- vative, then find the potential…

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Q: Find the potential function f for the field F. F= (4x3y10z10, 10x4y9z10 10x4y1029) O fix, y. 2) =…

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Q: 3x 3x Determine whether F(x, y) = e³ cos 3y i – e³ sin 3yj is a conservative vector field. If so,…

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Q: 2y Find the gradient field F = Vo for the potential function o = F =

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Q: 6. Consider the vector field F(ar, y) = (8a y+e")î+ (Ka4 + e")j, where K is some constant. -For…

A: Consider the vector field F(x,y)=8x3y+exi^+Kx4+eyj,^ where K is some constant. a…

Q: Consider F(x,y,z)=(e³+e²²)₁²+(e¹+z)j + (2xze²²+y)k. Please answer the items below including all…

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Q: 8. The component of the field F= (1,2,3) normal to the plane z = -3x + 3y -1 is (a) 0. (b) –2//19.…

A: If we are given a plane equation in the form Ax+By+Cz=D, then the normal vector to the plane will…

Q: 7. Determine if the given vector field F is conservative on some domain and, if it is, find the…

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Q: Find a potential function f for the field F. F = (2y+z)i + (2x + 5z)j + (x + 5y)k A general…

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Q: Given a scalar field f(x, y)= xy + x² and C is the curve defined by the equation y =-x². Calculate F…

A: Given scalar field  fx,y=xy+x2 and C is the curve defined by the equation y=-x2.

Q: Find the potential function f for the field F = 9x i+ 6y j+ 6z k. A general expression for the…

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Q: Q2: Find the work done S. F.dr in the force field F = yzî + xzĵ + xyk in moving from (1,1,1) to…

A: The equation of a line joining by the points and is given as the following.

Q: Which one of the following is a potential function of the following vector field? O f(x,y) = xy+2x O…

A: Find potential function

Q: da potential function f for the field F. F = (4y + 2z)i + (4x+z)j + (2x+y)k eneral expression for…

A: Topic:- application of integration

Q: Given: r = F| i = (x, y, 2) And letting F be the vector field F = f'/rP. Please solve in general the…

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Q: Find the potential function f for the CONservative vector field 言こ<2xe' x2+y? 2ge %3D fCx,y) e 2.…

A: The complete question is solved in next step

Q: 2 find the divcrgence and curl of the vectur field f gven by F p) f(xyz) =cas (2x)it X sin ryit z°k…

A: the given vector field F is: F(x,y,z)=cos2xi+2sinπyj+z2k we have to find the divergence and the curl…

Q: (b) For the case a = 3, b = 4, and for the constant vector field F(x,y,z) = 4 1 + k , find the flux…

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Q: Is the vector field F(x, y) = (sin(x)ely=3 + 2r cos(r>)y°, -2e)y-3 + 6 sin(x³)»*) conservative?…

A: Consider the given vector field.

Q: Find a potential function f for the field F. F = (3y + 5z)i + (3x + 4z)j + (5x + 4y)k A general…

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Q: 6. The component of the field F= (y,z,xy) normal to the cone ² = x +y° is (b) (xy– yz)/Vx² + y² +1.…

A: Given that : F= { y, z, xy } normal to the cone z2=x2+y2 is (b)

Q: Find a potential function f for the field F. F= (4y + 2z)i + (4x + 5z)j + (2x + 5y)k A general…

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Q: 2. Given that F(x, y, z) = (e, xey + e², ye²) is a conservative vector field. a. Find a potential…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find a potential function f for the field F = ev *2=(4 i + 4x j + 8x k). A general expression for…

A: We can calculate the following question by usual method of calculating potential function

Q: Find a potential function f for the field F. F = (4y + 5z)i + (4x + 3z)j + (5x+3y)k A general…

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Q: Find the potential function f for the field F. 6..6. F=7x°y°z' i+ 6x y°z'j+ 7x'y°z°k O A. f(x,y.z) =…

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Q: Q1(a) For which value of a the field v=(y-x)i +(2x- y)j + azk is solenoidal. (b) Find the gradient…

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Q: 2. Given F(x, y) = (4x³y² - 2xy³)i + (2x¹y − 3x²y² + 4y³)j is a - conservative vector field. a. Find…

A: To find the potential function for the given conservative vector field :-

Q: The slope field oY = f(t,y), with initial condition f(0) = 1, is shown. Find limf(t.y). dt - 10 「 ンン…

A: On the slope field draw the graphical solution with initial condition f(0)=1:

Q: Find the potential function f for the field F. F= i- k o f(x, y, z) = - 2 + c 2x o f(x, y, z) = - 2y…

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Q: Find a potential function f for the field F. F = (4y + 2z)i + (4x + 4z)j + (2x + 4y)k .... . A…

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Q: Let F = (e" sin y) i+ (e cos y + y)j. Answer the following questions. (a) show that is F…

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Q: 2z Find the gradient field of the function, g(x,y,z) = In (4x? + y?). The gradient field is Vg = (…

A: Solved below

Q: y + Find a potential function f for the field F = e*42(3 i + 3x j+ 12x k). A general expression for…

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Q: 2. Find the gradient field F = Vy for the potential function p. Sketch a few level curves of o and a…

A: Given φ(x,y)=2x2+4y2 The gradient field  F=∇·φ=∂φ∂x,∂φ∂y=4x,8y Some vectors of F are  At x=1 and y=1…

Q: Q2: Find the work done S. F.dr in the force field F = yzî + xzj + xyk in moving from || (1,1,1) to…

A: The given question is related with work done. We have to find the work done ∫CF→ . dr  in the force…

Q: Find the potential function for the following vector field F(x, y, z) = (2x cos y – 2z3) î + (29+…

A: F = &lt;2xcosy-2z3, 29+2ye2-x2siny, y2e2-6xz&gt; To check F¯ is conservative  not we have t check…

Q: Find the divergence of the field F. yj - xk F= 1/2 +: 2 OA. 3/2 2 -X O B. 3/2 2 X -y OC. 3/2 O D. 0

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Q: If 0(x,y) is a potential function for a constant vector field F = (a, b), then the graph of the…

A: The constant vector field is F=a, b. The equation of the function is z=ϕx, y

Q: 40. Find the circulation of the field F = yi + (x + 2y)j around each of the following closed paths.…

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Q: Question Which of the following is a potential function f for F(x, y, z) = (2x cos(v2). -x²z sin(yz)…

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Q: (b) A potential function for the vector field F (x, y) = (2x + 1)(x² + x + 1)² 7+ (2y + 1)(y² + y +…

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Q: Find a potential function f for the field F = e²y + 52 (2 i + 4x j + 10x k). A general expression…

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Q: Find a potential function f for the field F. 7y j+ y² +z? 7z 21 F = (In x+ sec(10x + 10y)) i+ sec…

A: Given that F = (ln(x) + sec^2 (10x + 10y)) * i + (sec^2 (10x + 10y) + (7y)/(y ^ 2 + z ^ 2)) * j +…

Q: Find a potential function f for the field F = e* * 3²( i+ 4x j+ 3x k). A general expression for the…

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Q: 25. Evaluate |F•T ds for the vector field F = x²i – yj along the curve x = y? from (4, 2) to (1,–1).

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